Ball mills with superellipsoidal balls

ABSTRACT

A BALL TYPE GRINDING MILL, IN WHICH THE BALLS ARE SUPERLLIPSOIDS OF SUCH A SHAPE THAT THE SURFACE OF THE BALL IN EACH OCTANT OF A CARTESIAN COORDINATE SYSTEM HAS X,Y AND Z AXES WHICH ARE DEFINED BY THE FORMULA-   (X/A)N+(Y/B)N+(Z/X)N=1,   WHEREIN A, B, C, N1, N2 ARE CONSTANTS, A IS UNEQUAL TO B, AND N1 N2 AND N3 EACH HAVE A MINIMUM VALUE GREATER THAN 2, PREFERABLY N1, N2 AND N3 EACH HAVE A MAXIMUM VALUE OF 4 AND MOST PREFERABLY IN THE RANGE 2.1-4.0. IT IS ALSO PREFERABLE THATY THE RATIO BETWEEN AT LEAST TWO OF THE CONSTANTS A,B AND C BE GREATER THAN 1 AND LESS THAN 2, AND MORE PARTICULARLY THE RATIO BETWEEN A AND B MAY ADVANTAGEOUSLY EQUAL 4 TO 3 WHEN B EQUALS C.

United States Patent 11 1 Hamilton et al.

[ BALL MILLS WITH SUPERELLIPSOIDAL BALLS [75] Inventors: Frank Alexander Hamilton, Dudley,

New South Wales; Thomas George Calcott, Mayfield, New South Wales, bothof Australia [73] Assignee: Commonwealth Steel Company Limited, Waratah, New South Wales, Australia 221 Filed: Oct. 6, 1971 211 Appl.No.: 187,049

[30] Foreign Application Priority Data Jan. 12,1968 Australia .......,,.32 310/6s [521 US. Cl. 241/176, 241/184 51] int. Cl. B026 17/10, B02 17/20 53 FieldofSearch.....241/170-178, 184;5l/164.5

[56] References Cited UNITED STATES PATENTS 1,133,368 3/1915 De Vilbiss 51/1645 FOREIGN PATENTS OR APPLICATIONS 246,653 4/1926 Italy 241/184 8/1961 Germany 51/1645 OTHER PUBLICATIONS Bell, R. J. T., An Elementary Treatise On Coordinate Geometry Of Three Dimensions, Macmillan & Co., Ltd., 1910, pp. 9 & 83, Sci. Lib. QA553B4.

Gardner, M.; Scientific American, ,Mathematical Games; Sept., 1965, pp. 222, 224, 226,228, 230, 232, 234; Sci. Lib. T1.S5.

Primary Examiner-Donald G. Ke lly Att0rney-Benjamin H. Sherman et al.

[57] ABSTRACT A ball type grinding mill, in which the balls are superellipsoids of such a shape that the Surface of the ball in each octant of a Cartesian coordinate system has x, y and z axes which are defined by the formula wherein a, b, c, 11,, n and n are constants, a is unequal to b, and n 11 and 11 each have a minimum value greater than 2. Preferably n n and n each have a maximum value of 4 and most preferably in the range 2.1-4.0. It is'also preferable that the ratio between at least two of-the constants a, b and c be greater than 1 and less than 2, and more particularly the ratio between a and b may advantageously equal 4 to 3 when b equals 6 Claims, 3 Drawing Figures This application is a continuation-in-part of our copending application Ser. No. 789,719, filed Jan. 8, 1969, now abandoned.

The invention relates to ball type grinding mills for the grinding of materials in either wet or dry state. The term ball is used as denoting the loose objects, also known as grinding media, within the rotating or otherwise moving part of the mill which perform the grinding operation. Such balls have heretofore been used in a variety of shapes.

Such balls may be made in'various manners, including forging, upsetting or molding, and the materials used to make such objects may be steel, flint, ceramic,

etc.

The balls have to be replaced from time to time because they wear away mechanically and are also sub ject to chemical corrosion, and this replacement is a considerable item'of expense.

The object of the present invention is to provide balls of a ball mill with improved shape which are more economical to manufacture and more efficient in operation.

A circle when modified in shape by partial symmetrical deformation from four equally spaced directions (whilst retaining an approximately or totally convex form) is known and herein referred to as a supercircle". Similarly, a symmetrically deformed ellipse is known 'and referred to as a super-ellipse, the supercircle being a special form of super-ellipse. Correspondingly shaped solid bodies are known and herein referred to as "super-spheres and super-ellipsoids.

Mathematically thegeneral formula for deriving a (three-dimensional) super-ellipsoid is as follows:

In this formula x, y and: are rectangular Cartesian where a does not equal b but where b may equal c. This may be regarded as a special form of the more general super-ellipsoid. Also, as in the derivation of any ellipsoid or super-ellipsoid, the powers n n and n need not be equal one to another.

For the purposes of the present invention a superellipsoid may therefore be defined as a derivative of the above general formula for all conditions other than "where 1 b c and m, n, and n each have a value equal to or less than 2.

The above stated general formula is valid, in such case! where n is not equal to a mul iple of v if the rmula is employed tederlve super-ellipsoid octant by eetent. That is, a complete super-ellipsoid may be derived to occupy a complete Cartesian space by eonltruetlng one eetent of the super-ellipsoid and reflec in time into the remalnlng'seven ectantn of the Cartelill'i space. Super-ellipsoids, hereinafter referred to in conjunction with the general formula should be understood as so constructed.

For the purpose of this invention, the value ofnn. is

e e t a .2. birtnrefe ah y. aetar e than 1 h;

shape of a super-ellipsoid for values of n greater than 4 approaching that of a cylinder.

The present invention therefore provides a ball type grinding mill in which the balls are of such ashape that the surface thereof in each octant ofta Cartesian coordinate system having x, y and z axes can be expressed by the formula drawings, in which FIG. 1 is an exemplary outline of a ball for use in a grinding mill according to the invention, and whichhas the shape of a super-ellipsoid,

FIG. 2 is a mathematical diagram embodying the outline of FIG. 1, and

FIG. 3 is a perspective view of an embodiment .ofa ball mill according to the invention, with partswcut away.

FIG. 1 may be regarded as a super-ellipse .perseuor as an elevation of a super-ellipsoid generated .by rotating the super-ellipse about its major axis. Also of course, it is a section on any plane passing through such major axis.

It is also possible to have the cross-section of the supenellipsoid along any plane at right angles to the longest axis as itself a super-circleuor .a supebellipse, although this may be more difficult to manufacture.

Referring now to FIG. 2, a pair of Cartesian axesare depicted having two co-ordinates x and y, and a superellipse curve is depicted at 10.

In such curve l0, and b are half axes of the curve, a being half of the major axis and b being half of the (minor) axis at right angles thereto.

The remaining Cartesian co'ordinate z and the remaining half axis c are not visible in FIG. 2,.being at right angles to the plane of the drawing sheet.

It has now been found in accordance with the invention that super-ellipsoids ashereinbefore definedare particularly efficient in the grinding of materialsin .ball mills. An example of a ball mill suitable forthe purpose is shown in general outline in FIG.3 and comprisesa drum D which is mounted in alined bearings 20,22 for rotation on a horizontal axis. The bearings are supported on base posts 24 and 26, respectively.

The drum D has an inlet or feed and portion 28 and an outlet or discharge end portion 30, and the portion of the drum between the bearings 20,22 comprises a middle cylindrical section 32 and twoconical end sections 34,36 which converge from said middle section 32 towards the inlet end portiortk28and the outletend portion 30, respectively. A gearwheel 38-is secured to the drum Hand is concentrical therewith. Said, gear wheel 38 is adapted for mashing engagement with a tion 32 is providedwith an opening covered by. a removable cover member 40. The drum D is tare-charged with a multiplicity of grinding mill balls 42 of the kind described above which may have been introduced through the feed end portion 28 or through the opening having the cover member 40 upon removal of said cover member.

In operation continuous rotary motion is imparted to the drum D by the motor (not shown) through the intermediary of the pinion (not shown) and the gear wheel 38. Material 44 to be treated in the ball mill, for example ore, is fed into the drum D through the feed end portion 28, usually continuously and with or without moistening liquid as required by the treatment process. Ordinarily the feed velocity is so adjusted that the combined volume of the grinding balls 42, the material 44 and any liquid that may be present is constantly less than approximately 45 percent of the interior volume of the drum D, whereby it is achieved that only smaller and lighter fractions of the material 44 escape through the discharge end portion 30 of the drum D, while heavier fractions gravitate toward the lower portion of the drum and are subjected to further grinding action.

I It may be mentioned that the actual grinding action caused by frictional surface engagement between the balls 42 and pieces of the material 44 and partially also between saidpieces themselves is usually augmented by a crushing impact action caused by balls 42 which are entrained by the interior walls of the rotating drum to a higher level and then drop down onto the main mass in the drum.

During the rotation of the ball mill the balls of the inventive shape tend to align themselves end to endand side by side which serves to delay wear and to preserve the shape even under wear. Also, the balls have a smaller peripheral dimension than spherical balls of the same weight and they thereby impart a greater amount of energy per unit area on impact with the material in the drum than spherical or avoid balls, as generally employed in the art. Furthermore, the individual balls are readily subjected to rotational movements in the drum, particularly about their longer axes.

For practical purposes the invention is restricted to the use of balls in the shape of super-ellipsoids in which n,, n and u each has a value of 2.1 to 4.0, and the ratio between the larger and smaller of at least one pair of semi-axes (a, b, c) lies between I and 2. A very desirable set of rati os is b/c; and a/b j/ We claim? l. A ball type grinding mill, in which the ballsare superellipsoids of such a shape that the surface of the ball in each octant of a Cartesian coordinate system has 1:, y and z axes which are defined by the formula a ll P ndi asset i i'thins a m 1,

wherein in, n and n each have a maximum value of 4.

3. A ball type grinding mill as set forth in claim 1, in which b equals 0.

4. A ball type grinding mill as set forth in claim 1, in which n n n 5. A ball type grinding mill as set forth claim 1, in which n,, n and u each have a value in the range 2.1-4.0 and the ratio between at least two of the constants a, b and c is greater than 1 and less than 2.

6. A ball type grinding mill as set forth in claim 3, in 

